As a theory of skill acquisition, the instance theory of automatization posits that, after a period of training, algorithm-based performance is replaced by retrieval-based performance. This theory has been tested using alphabet-arithmetic verification tasks (e.g., is A + 4 = E?), in which the equations are necessarily solved by counting at the…

This paper presents a model for mastery learning. The framework for this model overlays the cognitive and knowledge dimensions from Krathwohl's revision of Bloom's Taxonomy, the Revised Taxonomy, with Polanyi's theory of personal knowledge. A simplified framework integrates Polanyi's concepts of subsidiary and focal awareness with the Revised…

Spatial thinking has roles to facilitate learners to remember, understand, reason, and communicate objects and the connections among objects that are represented in space. This research aims to analyze the spatial thinking process of students in constructing new knowledge seen from the field-independent cognitive style learners based on…

The primary purpose of this paper is to introduce essential elements of cognitive information processing (CIP) theory, research, and practice as they existed at the time of this writing. The introduction that follows describes the nature of career choices and career interventions, and the integration of theory, research, and practice. After the…

An iterative unpacking strategy consists of sequencing empirically-based theoretical developments so that at each step of theorizing one theory serves as an overarching conceptual framework, in which another theory, either existing or emerging, is embedded in order to elaborate on the chosen element(s) of the overarching theory. The strategy is…

This study explores the effects of the "presence of external representations of a mathematical object" (ERs) on problem solving performance associated with short double-choice problems. The problems were borrowed from secondary school algebra and geometry, and the ERs were either formulas, graphs of functions, or drawings of geometric…

From the 1990s until 2017 the High Ability and Inquiry Research Group (HAIR) at McGill University in Montreal, received C$1.3M in research funds from Canadian, Quebec, and US agencies to support its research and graduate training in education and educational psychology. Their research encompassed two principal areas, Inquiry in Education and…

In this article, the author wishes to emphasize two fundamental points related to theory that were significantly underplayed in Simon et al.'s "A Developing Approach to Studying Students' Learning through Their Mathematical Activity" (2010). The author believes these points are central to any study of children's mathematical learning. The first…

The objective of this paper was to develop a four dimensions dynamic model for designing instructional activities appropriate to electronic and virtual learning environments. The suggested model is guided by learning principles of cognitivism, constructivism, and connectivism learning theories in order to help online learners to build and acquire…

Efficacy of a teaching strategy technically refers to the ability of that strategy to produce a desired or intended learning outcomes. To date, there is little information on the efficacy of social media technologies in academia and it is likely to be some time before their effectiveness is proven. It is therefore legitimate to ask the question,…

Successful learning sometimes requires that the learner abandons or rejects one or more prior concepts, beliefs, or intuitive theories. Such "nonmonotonic changes" are widely believed to have a low probability of occurring spontaneously and to be difficult to promote with instruction. A theory of nonmonotonic cognitive change should explain both…

Contradictory evidence has been reported on the effects of discovery learning approach and the role of instructional explanations. By manipulating the presence of instruction (verbal explanation) and transparency of problem structures, we investigated how effects of instructional explanations differed depending on the transparency of problem…

Though the No Child Left Behind Act of 2001 requires secondary students with Asperger's syndrome (AS) to take high-stakes mathematical tests, many students with AS exhibit weaknesses in mathematical and executive functioning skills. The purpose of this mixed-methods case study was to explore the use of differentiated mathematical strategies with…

Early Childhood Education (EDE) describes the education of young children from birth through age 8. EDE reports have concluded that traditional approaches to curriculum, such as those emphasizing drill and practice of isolated, academic skills, are not in line with current knowledge of human learning and neuropsychology. These approaches fail to…

Many types of learning require the mapping of information across situations. The proposed organizational framework extends the cognitive study of mappings across problems to include mappings across representations, solutions, and sociocultural contexts. I apply one-to-one, one-to-many, and partial mappings to analyze representative cases that…